Use our free GCF of Fractions Calculator tool to compute the GCF of 121/270, 765/192 i.e 1/8640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 121/270, 765/192.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 121/270,765/192
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 121/270,765/192, numerators are 121,765
Denominators are 270,192
The GCF of 121,765 is 1 .
LCM of 270,192 is 8640.
The greatest common factor of 121/270,765/192 = [GCF of 121,765]/[LCM of 270,192]= 1/8640
Therefore, the GCF of 121/270,765/192 is 1/8640.
To find the highest common factor of 121,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 121 are 1, 11, 121
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 121,765 is 1.
Lets's calculate GCF of 121,765
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 121
:1,11,121
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 121,765 . The biggest common factor number is the GCF number.
So the greatest common factor 121,765 is 1.
Lets's calculate LCM of 270,192
2 | 270, 192 |
3 | 135, 96 |
45, 32 |
∴ So the LCM of the given numbers is 2 x 3 x 45 x 32 = 8640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8640
Therefore, the GCF of Fractions 121/270,765/192 is 1/8640
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 270,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,192) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(270,192) x common factors =6 x 1 = 6
LCM(270,192) = ( 270 × 192 ) / 6
LCM(270,192) = 51840 / 6
LCM(270,192) = 8640
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 121,765?
The HCF of 121,765 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 121/270, 765/192?
Answer: GCF of Numerators as per given numbers 121/270, 765/192 is
GCF of Numerators i.e. for 121,765 is 1
LCM of denominators i.e. for 270,192 is 8640.
Thus, GCF of Fractions is 1/8640.Finally, GCF of Fractions for 121/270, 765/192 is 1/8640.